Question

Find the modulus of the complex number 2 — 5i.

Answer 1

Hint: In these types of questions always remember the basic formula of modulus. If complex number is given as a + ib then modulus of a complex number=\[|Z| = \sqrt {{a^2} + {b^2}} \]. Use this formula to get the required answer.

Complete step-by-step answer:
Here we have a complex number whose value is 2 — 5i
Let Z= 2— 5i ---(equation 1)
On comparing with general form a=2 and b=(-5).
Now let’s use the basic formula of finding a modulus of a complex number=\[|Z| = \sqrt {{a^2} + {b^2}} \]
$\Rightarrow$ |Z|=\[\sqrt {{{(2)}^2} + {{( - 5)}^2}} \]
$\Rightarrow$ |Z|=\[\sqrt {4 + 25} \]
$\Rightarrow$ |Z|=\[\sqrt {29} \]
Hence \[\sqrt {29} \] is the modulus of the complex number 2 — 5i.

Note: In these types of questions first identify the a and b in the complex number then use the basic formula of finding the modulus of the complex number i.e. \[|Z| = \sqrt {{a^2} + {b^2}} \] and put the correct values in the formula for finding the modulus and simplify the value of modulus.